Provably Robust Boosted Decision Stumps and Trees against Adversarial Attacks
This work addresses adversarial robustness for boosted trees and stumps, a critical issue for practitioners using models like XGBoost, though it is incremental in extending robustness methods to these specific models.
The paper tackles the problem of adversarial robustness for boosted decision stumps and trees, which are widely used but previously lacked provable robustness results. It shows that exact min-max robust loss can be computed efficiently for stumps, and achieves state-of-the-art robust test errors on datasets like MNIST (12.5% for ε∞=0.3), FMNIST (23.2% for ε∞=0.1), and CIFAR-10 (74.7% for ε∞=8/255), competitive with robust convolutional networks.
The problem of adversarial robustness has been studied extensively for neural networks. However, for boosted decision trees and decision stumps there are almost no results, even though they are widely used in practice (e.g. XGBoost) due to their accuracy, interpretability, and efficiency. We show in this paper that for boosted decision stumps the \textit{exact} min-max robust loss and test error for an $l_\infty$-attack can be computed in $O(T\log T)$ time per input, where $T$ is the number of decision stumps and the optimal update step of the ensemble can be done in $O(n^2\,T\log T)$, where $n$ is the number of data points. For boosted trees we show how to efficiently calculate and optimize an upper bound on the robust loss, which leads to state-of-the-art robust test error for boosted trees on MNIST (12.5% for $ε_\infty=0.3$), FMNIST (23.2% for $ε_\infty=0.1$), and CIFAR-10 (74.7% for $ε_\infty=8/255$). Moreover, the robust test error rates we achieve are competitive to the ones of provably robust convolutional networks. The code of all our experiments is available at http://github.com/max-andr/provably-robust-boosting